XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,470,432

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/24/2016, 1:57:46 PM Β· Difficulty 10.7275 Β· 5,343,928 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
3385e00661dfc9a2eb2e8442dac77e705a5a468a6306bdc6227702ab010c9667
View on Chainz β†—

Height

#1,470,432

Difficulty

10.727513

Transactions

2

Size

1.14 KB

Version

2

Bits

0aba3e46

Nonce

184,495,816

Timestamp

2/24/2016, 1:57:46 PM

Confirmations

5,343,928

Mined by

⛏️ P2SHAN58L23KesdsGdBYEj8WfnLLtbYv7bUQRR

Merkle Root

0b98bf323140b73629774461a951d4bd093c61218232490ecb9fbdb6ffc60c4c
Transactions (2)
Coinbase9f35a9f88042a6…9bfc8d9574f176
1 in β†’ 1 out8.6900 XPM109 B
AN58L23K…Yv7bUQRR
ba1a05968cef2f…ac75001e8a7d5e
6 in β†’ 2 out9.5800 XPM964 B
ATkvSe4R…5PpU2iczAesJVMS3…WrAkHdm5
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

8.418 Γ— 10⁹⁷(98-digit number)
84182429522678829616…98715574759226982399
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
8.418 Γ— 10⁹⁷(98-digit number)
84182429522678829616…98715574759226982399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.418 Γ— 10⁹⁷(98-digit number)
84182429522678829616…98715574759226982401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.683 Γ— 10⁹⁸(99-digit number)
16836485904535765923…97431149518453964799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.683 Γ— 10⁹⁸(99-digit number)
16836485904535765923…97431149518453964801
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
3.367 Γ— 10⁹⁸(99-digit number)
33672971809071531846…94862299036907929599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.367 Γ— 10⁹⁸(99-digit number)
33672971809071531846…94862299036907929601
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
6.734 Γ— 10⁹⁸(99-digit number)
67345943618143063693…89724598073815859199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.734 Γ— 10⁹⁸(99-digit number)
67345943618143063693…89724598073815859201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
1.346 Γ— 10⁹⁹(100-digit number)
13469188723628612738…79449196147631718399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.346 Γ— 10⁹⁹(100-digit number)
13469188723628612738…79449196147631718401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,758,946 XPMΒ·at block #6,814,359 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy